In the context of a wireless communication system, as for instance the Universal Mobile Telecommunications System (UMTS), scheduling can be formulated in terms of a preference function fk that is calculated for at least one transmission channel out of k=1, . . . ,K transmission channels for a block of substantially orthogonal resources (e.g. frequency, subcarriers, spreading codes, time slots, spatial/polarization eigenmodes) to be scheduled simultaneously. The transmission channel or channels that have the largest value of fk, or a value of fk that is above some pre-defined limit are used for transmitting data using the scheduled resources. In this context, a transmission channel k may for instance describe the physical propagation channel between a single- or multi-antenna transmitter and a single- or multi-antenna receiver. There may be only one or several transmitters, and, correspondingly, there may be one or several receivers. Said transmitters and receivers may represent base stations, mobile stations or relay stations of a wireless communication system. A transmission channel k can be defined for both the up- and and downlink. A transmission channel k may further relate to a channel between only a sub-group of transmit antenna elements of a multi-antenna transmitter and a single- or multi-antenna receiver, or to a channel between a single or multi-antenna transmitter and a sub-group of antenna elements of a receiver.
The preference function fk for a transmission channel k may be of the form:fk=f(u, dk, zk, hk, ck, CQImk, CQIek, CQISk, . . . )
Here, u is a parameter that describes the general status of the transmission queue, and the remaining parameters are specific for the transmission channel k=1, . . . ,K. Thus dk is the delay experienced by transmission channel k, i.e. the time that the next packet for/from transmission channel k has spent in the queue, zk is the size of the next packet scheduled for her (or scheduled by her for transmission, in uplink operation), hk describes the history, taking into account the amount of data transmitted via transmission channel k during the immediate past, and ck is her possible priority class, possibly based on the type of subscription or terminal, and/or the type of data. The link-specific Channel Quality Indicators (CQI) that scheduling may be based on, are                CQImk, which determines the transmission mode of transmission channel k. The mode selection may be based on side information, based on measurements at the transmitter, or feedback from a receiver. In particular, CQImk determines the rate of transmission channel k, and possibly the used feedback-based beamforming, the Adaptive Space-Time Modulation scheme chosen (matrix/vector modulation, space-time coding), the rate of the concatenated channel code, and/or the modulation alphabets.        CQIek, which indicates the expected error rate of the transmission mode indicated by CQImk, and        CQIsk, which indicates the speed of transmission channel k, i.e. the channel coherence time.        
Based on these parameters (or a subset of them), a scheduler can decide which transmission channel is suited for data transmission, taking into account overall throughput, fairness, delays etc., when applicable. The parts of fk that do not depend on the radio link are the domain of higher layer protocols. The CQIs, however, are in intimate relationship to the physical layer, and are to be designed in accordance to the physical layer algorithms.
When considering the physical layer, the preference functions fk may be used in order to minimize the transmission power, maximize the rate, or optimize performance. Often, the physical and higher layer algorithms involve an automatic retransmission request (ARQ) protocol. In these cases, maximizing system capacity typically requires that the frame or block error rate is close to a given optimal value. Thus the preference functions fk may be used to choose the transmission channel that provides the highest rate with the maximum allowed transmission power, reaching a target error performance.
If scheduling is based on CQIek, i.e. CQIs that correlate with the expected error performance, the most clear cut way to measure the performance of scheduling is to measure the performance of selection diversity. This means that a number K of transmission channels are considered that have some type of channel statistics. Due to this statistical nature of the K transmission channels, scheduling for example one specific transmission channel out of the K transmission channels that actually has the optimum transmission channel characteristics, for instance the lowest fading or path loss, for data transmission achieves superior performance as compared to transmitting on an arbitrarily chosen transmission channel. Thus, as multi-user diversity is available to a transceiver in a communication system with multiple users to receive or transmit signals, or antenna diversity is available to a receiver that deploys multiple antenna elements to receive a signal that has been transmitted by a transmitter using only a subset of the multiple receiver elements or to transmit a signal using only a subset of the multiple transmitter elements, or frequency diversity is available when a signal is transmitted at different portions of the available channel bandwidth, selection diversity is available for the scheduler when it is offered the degree of freedom to choose from a variety of transmission channels between different transceivers or their elements.
For optimal performance of selection diversity, the transmission channel with the lowest predicted bit error rate (BER) may be scheduled for transmission. This results in a decreased average error rate. However, for a Multiple-Input-Multiple-Output (MIMO) channel, scheduling based on direct evaluation of BER requires heavy computation.
Prior art document “On transmit diversity and scheduling in wireless packet data” by A. G. Kogiantis, N. Joshi, and O. Sunay, published in IEEEcomm, June 2001, vol. 8, pp. 2433-2437, discloses scheduling in a Multiple-Input-Single-Output (MISO) channel, wherein, among others, an orthonormal diversity transmission scheme (Space-Time Transmit Diversity, STTD) is compared to a single-antenna transmission scheme without diversity. In both schemes, a transmitter (either with two transmit antennas and STTD or with a single antenna) schedules one out of K transmission channels, wherein each respective transmission channel is defined by the physical propagation channel between the two or one transmit antennas at the transmitter and the single antenna at the respective receiver, for a data transmission, wherein scheduling is based on the maximum Carrier-to-Interference power ratio (C/I) for each transmission channel.
The STTD scheme as deployed in the Kogiantis reference can be considered as a matrix modulation scheme, which may be defined as a mapping of modulation symbols onto non-orthogonal spatial resources and orthogonal resources, as for instance time slots or symbol periods, frequency carriers, orthogonal codes, etc., or any combination of these.
In matrix modulation schemes, diversity may be applied. For instance, in a space-time matrix modulation scheme, at least one of said modulation symbols may be mapped to a first antenna element in a first symbol period and to a second antenna element in a second symbol period. Similarly, in a space-frequency matrix modulation scheme, at least one of said modulation symbols may be mapped to a first antenna element and transmitted with a first carrier frequency and to a second antenna element and transmitted with a second carrier frequency.
If modulation symbols are mapped to the non-orthogonal spatial resources only, so-called vector modulation is performed, and only spatial diversity is available.
In the sequel of this introduction, space-time matrix modulation methods will be presented as an example of orthonormal and non-orthonormal matrix modulation methods. The orthogonal resource is then represented by the T symbol periods (or time slots) to which a block of data symbols is mapped. However, the presented matrix modulation methods are readily applicable to matrix modulation that employs the frequency domain, the code domain, the eigenmode domain or polarization domain as orthogonal resource instead of the time domain.
A space-time matrix modulator employing Nt transmit antennas and T symbol periods is defined by a TXNt modulation matrix X. The modulation matrix X is a linear function of the Q complex-valued modulation symbols xn, n=1, . . . ,Q to be transmitted by the Nt-antenna transmitter during T symbol periods. Modulation symbols may for instance obey the Binary Phase Shift Keying (BPSK), Quaternary Phase Shift Keying (QPSK) or Quadrature Amplitude Modulation (QAM) symbol alphabet. The modulation matrix X thus basically defines when modulation symbols xn, with n=1, . . . ,Q and/or functions of said modulations symbols xn such as −xn, xn+ or −xn+ are transmitted from which transmit antenna nt=1, . . . ,Nt at which time instance t=1,. . . ,T. In this context, the superscript operator “*” denotes the conjugate-complex of a complex number. The matrix modulation then can be understood as a mapping of modulation symbols and functions thereof to Nt respective data streams that are transmitted by Nt respective transmit antenna elements of a transmit antenna during T symbol periods. For the STTD scheme as applied in the Kogiantis reference, the modulation matrix X is defined according to the so-called Alamouti Space-Time code with T-2 and Nt=2 as
                    X        =                              [                                                                                x                    1                                                                                        x                    2                                                                                                                    -                                          x                      2                      *                                                                                                            x                    1                    *                                                                        ]                    .                                    (        1        )            
With Nk,r receive antennas at the reception side of the transmission channel k, the signal model reads as:Yk=X·Hk+Nk,  (2)wherein Yk is a TXNk,r matrix of signals yk,ij received at receive antenna element j=1, . . . ,Nk,r during symbol period i=1, . . . ,T, wherein the elements hk,ij with i=1, . . . ,Nt and j=1, . . . ,Nk,r of the NtXNk,r channel matrix Hk define the flat fading propagation channel between transmit antenna element i and receive antenna element j, and wherein the TXNk,r matrix Nk,r represents the noise received in symbol period t=1, . . . ,T at receive antenna element nk=1, . . . ,Nk,r.
Lumping together the effects of matrix modulation as defined by the matrix X and the propagation effects as defined by the channel matrix Hk yields a complex-valued TNk,rXQ equivalent channel matrix Gk with an equivalent signal model:yk=Gk·x+nk,  (3)wherein the TNk,r-dimensional vector yk contains the signals received during T symbol periods at the Nk,r receive antenna elements at the reception side of transmission channel k, or functions thereof such as the conjugate-complex receive signal, the negative receive signal or the negative conjugate-complex receive signal; the Q-dimensional vector x contains the Q complex-valued modulation symbols xn, n=1, . . . ,Q that are modulated by the matrix modulation onto Nt transmit antenna elements in T symbol periods; and the TNk,r-dimensional vector nk contains the noise received at the receive antenna elements during the T symbol periods.
For the STTD scheme, the equivalent channel matrix Gk has the following shape:
                                          G            k                    =                      [                                                                                h                                          k                      ,                      11                                                                                                            h                                          k                      ,                      21                                                                                                                                        h                                          k                      ,                      21                                        *                                                                                        -                                          h                                              k                        ,                        11                                            *                                                                                            ]                          ,                            (        4        )            and the equivalent system model reads as
                              (                                                                      y                                      k                    ,                    11                                                                                                                        y                                      k                    ,                    21                                    *                                                              )                =                                            [                                                                                          h                                              k                        ,                        11                                                                                                                        h                                              k                        ,                        21                                                                                                                                                        h                                              k                        ,                        21                                            *                                                                                                  -                                              h                                                  k                          ,                          11                                                *                                                                                                        ]                        ·                          (                                                                                          x                      1                                                                                                                                  x                      2                                                                                  )                                +                                    (                                                                                          n                                              k                        ,                        11                                                                                                                                                        n                                              k                        ,                        21                                                                                                        )                        .                                              (        5        )            
It is readily seen from equation (5) that both the effects of matrix modulation and channel propagation are now contained in the equivalent channel matrix Gk, so that in the equivalent signal model of equation (5), the original modulation symbols xn and not functions of the modulation symbols xn are multiplied with the equivalent channel matrix Gk. With the equivalent channel matrix Gk, the Equivalent Channel Correlation Matrix (ECCM) Rk can be defined asRk=GkH·Gk,  (6)wherein the superscript operator “H” denotes the Hermitian conjugate of a matrix.
For the STTD scheme, it is easily seen that the ECCM is a diagonal matrix with
      R          k      ,      STTD        =            [                                                                                                                          h                                          k                      ,                      11                                                                                        2                            +                                                                                      h                                          k                      ,                      21                                                                                        2                                                          0                                                0                                                                                                                      h                                          k                      ,                      11                                                                                        2                            +                                                                                      h                                          k                      ,                      21                                                                                        2                                                        ]        .  
The ECCM can be interpreted as applying a matched filter to the equivalent channel matrix Gk, so that a matched filer estimate of the vector x that contains the Q modulation symbols xn with n=1, . . . ,Q is obtained as{circumflex over (x)}=GkH·yk=Rk,STTD·xk+GkH·nk,
When the power of the noise contribution nk can be neglected as compared to the power of the receive signal yk, the matched filter estimate {circumflex over (x)} is basically given by the term Rk,STTD·xk, i.e. the matched filter estimates {circumflex over (x)}n are simply the modulation symbols xn scaled by a real-valued factor |hk,11|2+|hk,21|2 that is identified as the sum of the powers of the channels hk,ij between the i=1, . . . ,Nt transmit antennas and the i=1, . . . ,Nk,r receive antennas.
The ECCM according to the STTD matrix modulation scheme only has non-zero entries on the main diagonal and thus does not cause self-interference between modulation symbols xn in the matched filter estimates {circumflex over (x)}n. Moreover, the diagonal elements are all equal, thus the ECCM is proportional to the identity matrix. Matrix modulation schemes with ECCM proportional to the identity matrix will be denoted as orthonormal matrix modulation schemes in the sequel, whereas matrix modulation schemes with ECCMs not proportional to the identity matrix will be denoted as non-orthonormal matrix modulation schemes.
FIGS. 1 and 2 show the essential features regarding scheduling in a selection diversity setting with STTD as disclosed in the Kogiantis reference. In particular, scheduling performance is investigated with orthonormal matrix modulation (STTD, Nt=2) and without matrix modulation (Nt=1) for Nk,r=1 and different numbers of transmission channels K, wherein the selection of a transmission channel for a data transmission is based on the maximum C/I at the reception side of that transmission channel.
FIG. 1 shows the scheduling performance in terms of log10 (BER) as a function of the ratio Eb/N0 of energy per bit Eb and noise power density N0 (assuming an Additive White Gaussian Noise (AWGN) process at the reception side of the transmission channel) in dB. Results for QPSK modulation and independent identically distributed (i.i.d.) flat Rayleigh-fading channels are depicted in separate figures for K=1, 2, 4 and 8 transmission channels with (dashed line) or without STTD (solid line), respectively.
It is observed that when there are up to K=4 transmission channels, scheduling with STTD outperforms scheduling without transmit diversity, because the (uncoded) BER with STTD is significantly smaller than the (uncoded) BER without STTD across the complete Eb/N0 regime. However, for K=8 transmission channels, scheduling without STTD outperforms STTD-based scheduling up to a BER 10−3. In the high Eb/N0 regime, the transmit diversity of STTD still gives better performance.
The reason for this can be seen in FIG. 2, where Probability Distribution Functions (PDFs) of the Signal-to-Noise Ratio (SNR) at the scheduled receiver (with Maximum Ratio Combining (MRC) for STTD) are plotted for i.i.d. Rayleigh fading channels hk,ij with E{|hk,i1|2}=1, once again for the cases with (dashed line) and without STTD (solid line) and for different numbers of transmission channels K=1, 2, 4 and 8 among which scheduling is performed. It can be clearly seen from the reduced extension and the pronounced maxima of the PDFs how STTD reduces the fluctuations in channel power. Also, it is evident that STTD is not able to change the average SNR of the channel, it just improves bad channels with the price of making good ones worse. Thus a significant portion of transmission channels, that have a strong channel from one transmit antenna and a weak from the other, have worse received SNR after MRC combining (see FIG. 2, upper left corner). With an increasing number K of transmission channels, a non-STTD transmission can always be scheduled to a transmission channel that would have had a worse channel if STTD was applied. Thus for multiple transmission channels K, scheduling without STTD works better.
The situation regarding combinations of orthonormal matrix modulation (STTD) and scheduling as disclosed in the Kogiantis reference can thus be summarised as:
For more than K=5 transmission channels, orthonormal matrix modulation (STTD) performs worse than a single antenna transmission as a component in a selection diversity scheme with max C/I-based scheduling, at BER 10−3.
If more than K=3 transmission channels are scheduled simultaneously, STTD and other orthonormal matrix modulations are of no practical use.